Phase Shift: Sliding

Subtract a number inside the bracket and the wave slides along the axis. $y = \sin\left(x-\frac{\pi}{2}\right)$ does at x what the sine did π/2 earlier, so every point of the sine graph turns up π/2 later: the wave has slid π/2 to the right. Its crossing going up is now at π/2 instead of 0.

The slide is the phase shift. y = sin(x − h) starts at x = h, where the inside is 0. For a positive h, a minus inside slides the wave right and a plus slides it left: sin(x + h) is sin(x − (−h)), which starts at −h. This sign is the classic slip, so always read the x that makes the inside zero.